How do I clean up unintended mesh inside a mesh?
Your mesh is really a mess. 

I think the method I show here can help you with it.

In Edit mode, wireframe view, use the border select to select the up and bottom parts.

Hide them or invert the selection.

In case you use HIDE: Select all the rest and separate it (do not delete it because you can need it later ).

Now the interior is a separated mesh.

See the image below.